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normal_inverse_gaussian.rs
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normal_inverse_gaussian.rs
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use crate::{Distribution, Float, InverseGaussian, Standard, StandardNormal};
use rand::Rng;
/// Error type returned from `NormalInverseGaussian::new`
#[derive(Debug, PartialEq)]
pub enum Error {
/// `alpha <= 0` or `nan`.
AlphaNegativeOrNull,
/// `|beta| >= alpha` or `nan`.
AbsoluteBetaNotLessThanAlpha,
}
/// The [normal-inverse Gaussian distribution](https://en.wikipedia.org/wiki/Normal-inverse_Gaussian_distribution)
#[derive(Debug)]
pub struct NormalInverseGaussian<N> {
alpha: N,
beta: N,
inverse_gaussian: InverseGaussian<N>,
}
impl<N: Float> NormalInverseGaussian<N>
where StandardNormal: Distribution<N>
{
/// Construct a new `NormalInverseGaussian` distribution with the given alpha (tail heaviness) and
/// beta (asymmetry) parameters.
pub fn new(alpha: N, beta: N) -> Result<NormalInverseGaussian<N>, Error> {
if !(alpha > N::from(0.0)) {
return Err(Error::AlphaNegativeOrNull);
}
if !(beta.abs() < alpha) {
return Err(Error::AbsoluteBetaNotLessThanAlpha);
}
let gamma = (alpha * alpha - beta * beta).sqrt();
let mu = N::from(1.) / gamma;
let inverse_gaussian = InverseGaussian::new(mu, N::from(1.)).unwrap();
Ok(Self {
alpha,
beta,
inverse_gaussian,
})
}
}
impl<N: Float> Distribution<N> for NormalInverseGaussian<N>
where
StandardNormal: Distribution<N>,
Standard: Distribution<N>,
{
fn sample<R>(&self, rng: &mut R) -> N
where R: Rng + ?Sized {
let inv_gauss = rng.sample(&self.inverse_gaussian);
self.beta * inv_gauss + inv_gauss.sqrt() * rng.sample(StandardNormal)
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_normal_inverse_gaussian() {
let norm_inv_gauss = NormalInverseGaussian::new(2.0, 1.0).unwrap();
let mut rng = crate::test::rng(210);
for _ in 0..1000 {
norm_inv_gauss.sample(&mut rng);
}
}
#[test]
fn test_normal_inverse_gaussian_invalid_param() {
assert!(NormalInverseGaussian::new(-1.0, 1.0).is_err());
assert!(NormalInverseGaussian::new(-1.0, -1.0).is_err());
assert!(NormalInverseGaussian::new(1.0, 2.0).is_err());
assert!(NormalInverseGaussian::new(2.0, 1.0).is_ok());
}
#[test]
fn value_stability() {
fn test_samples<N: Float + core::fmt::Debug, D: Distribution<N>>(
distr: D, zero: N, expected: &[N],
) {
let mut rng = crate::test::rng(213);
let mut buf = [zero; 4];
for x in &mut buf {
*x = rng.sample(&distr);
}
assert_eq!(buf, expected);
}
test_samples(NormalInverseGaussian::new(2.0, 1.0).unwrap(), 0f32, &[
0.6568966, 1.3744819, 2.216063, 0.11488572,
]);
test_samples(NormalInverseGaussian::new(2.0, 1.0).unwrap(), 0f64, &[
0.6838707059642927,
2.4447306460569784,
0.2361045023235968,
1.7774534624785319,
]);
}
}